1 Rapid bedrock uplift in the Antarctic Peninsula explained by viscoelastic response to
2 recent ice unloading
3
4 Grace A. Nielda*, Valentina R. Barlettab, Andrea Bordonic, Matt A. Kingd,a, Pippa L.
5 Whitehousee, Peter J. Clarkea, Eugene Domackf, Ted A. Scambosg, Etienne Berthierh
6
7 aSchool of Civil Engineering and Geosciences, Newcastle University, Newcastle upon Tyne,
8 UK.
9 bDTU Space, Technical University of Denmark, Lyngby, Denmark.
10 cDTU Physics, Technical University of Denmark, Lyngby, Denmark; DTU Compute,
11 Technical University of Denmark, Lyngby, Denmark.
12 dSchool of Land and Food, University of Tasmania, Hobart, Australia.
13 eDepartment of Geography, Durham University, Durham, UK.
14 fDepartment of Geoscience, Hamilton College, 198 College Hill Road, Clinton New York,
15 USA 13323; now at: College of Marine Science, University of South Florida, St. Petersburg,
16 Florida, USA.
17 gNational Snow and Ice Data Center, CIRES, University of Colorado, Boulder, Colorado,
18 USA.
19 hCentre National de la Recherche Scientifique, LEGOS, Université de Toulouse, Toulouse,
20 France.
21 *Corresponding author. E-mail address: [email protected]. Tel.:+44 (0)191 222
22 6323.
23
1
24
25 Abstract
26 Since 1995 several ice shelves in the Northern Antarctic Peninsula have collapsed and
27 triggered ice-mass unloading, invoking a solid Earth response that has been recorded at
28 continuous GPS (cGPS) stations. A previous attempt to model the observation of rapid uplift
29 following the 2002 breakup of Larsen B Ice Shelf was limited by incomplete knowledge of
30 the pattern of ice unloading and possibly the assumption of an elastic-only mechanism. We
31 make use of a new high resolution dataset of ice elevation change that captures ice-mass loss
32 north of 66°S to first show that non-linear uplift of the Palmer cGPS station since 2002
33 cannot be explained by elastic deformation alone. We apply a viscoelastic model with linear
34 Maxwell rheology to predict uplift since 1995 and test the fit to the Palmer cGPS time series,
35 finding a well constrained upper mantle viscosity but less sensitivity to lithospheric thickness.
36 We further constrain the best fitting Earth model by including six cGPS stations deployed
37 after 2009 (the LARISSA network), with vertical velocities in the range 1.7 to 14.9 mm/yr.
38 This results in a best fitting Earth model with lithospheric thickness of 100–140 km and
39 upper mantle viscosity of 6 × 1017 – 2 × 1018 Pa s - much lower than previously suggested for
40 this region. Combining the LARISSA time series with the Palmer cGPS time series offers a
41 rare opportunity to study the time-evolution of the low-viscosity solid Earth response to a
42 well-captured ice unloading event.
43
44 Key Words: Antarctic Peninsula, Larsen B, ice-mass loss, viscoelastic uplift, GPS, upper
45 mantle viscosity.
46
47
2
48 1. Introduction
49 Rapid changes in climate in the Antarctic Peninsula (AP) over the past 50 years have led
50 to the retreat and eventual collapse of several major ice shelves (Fig. 1), such as Prince
51 Gustav and Larsen A in 1995 (Rott et al., 1996), and Larsen B in 2002 (Rack and Rott 2004)
52 (see Cook and Vaughan (2010) for a complete summary). In response to ice shelf collapse,
53 tributary glaciers have exhibited acceleration and thinning (e.g., De Angelis and Skvarca
54 2003; Rignot et al., 2004; Scambos et al., 2004) and this dynamic ice loss induces a solid
55 Earth response which may be observed in GPS records.
56 The study of Thomas et al. (2011) identified markedly-increased uplift in GPS coordinate
57 time series from the Northern Antarctic Peninsula (NAP) that they associated with ice
58 unloading related to the breakup of Larsen B Ice Shelf in 2002. This uplift was best captured
59 in the near-continuous cGPS record at Palmer station which exhibited an increase in uplift
60 rate from 0.1 mm/yr prior to 2002.2, to 8.8 mm/yr thereafter. Thomas et al. (2011) suggested
61 that the effect was due to the elastic response of the solid Earth but they were not able to
62 satisfactorily reproduce the increased uplift rates with an elastic model, which they suggested
63 was at least partly due to the weakly defined magnitude and spatial pattern of ice-mass loss in
64 their model.
65 The NAP lies in a complex tectonic setting which passes from active subduction along the
66 South Shetland Trench, located north of the South Shetland Islands, to passive margin west of
67 65°W at the intersection of the Hero Fracture Zone with the Shetland Platform (see Fig. S1 in
68 the supplementary material). The Bransfield Basin separates the South Shetland Islands from
69 the NAP and has active volcanism along a mid-axial region, suggesting a back arc tectonic
70 setting (Barker and Austin 1998; Barker et al., 1991). The conversion from active subduction
71 to passive margin, and hence mantle conditions more likely reflective of low viscosity, took
72 place relatively recently at ~4 Ma before present along the AP margin just south of Hero
3
73 Fracture Zone (Barker et al., 1991). One of the GPS stations used in this study (ROBI, see
74 Section 2.1) lies along a presumed incipient rift axis as expressed by the active volcanic chain
75 of the Seal Nunataks (González-Ferrán 1983). However, there is little known in relation to
76 the mantle or crustal configuration beneath the Seal Nunatak region. The reader is referred to
77 Barker (1982) and Larter and Barker (1991) for a full tectonic history of the region. Due to
78 the active tectonic setting of the region, the mantle is likely to have a relatively low viscosity
79 compared with other locations undergoing deformation in response to changes in ice-mass
80 e.g. East Antarctica or Fennoscandia. Using a combination of inferred ice history, GPS and
81 GRACE data, Ivins et al. (2011) suggested this region has a relatively thin lithosphere (20-
82 45 km) and a low viscosity mantle (3-10 × 1019 Pa s). Due to the low viscosity nature of the
83 upper mantle, the Earth’s viscous response to ice-mass change in the AP is much more rapid
84 than in other regions of Antarctica, and post-1995 unloading events may hence be
85 contributing to the observed uplift in the NAP through viscoelastic rebound. Likewise,
86 assuming a Maxwell rheology, there may be very little, to no, residual response of the NAP
87 to unloading events associated with recession from the Last Glacial Maximum.
88 In this study we use cGPS data from the NAP to constrain a local model of solid Earth
89 response to a high resolution present-day mass loss field (Scambos et al., 2014, in review).
90 By comparing the modelled elastic uplift time series with the observed cGPS uplift time
91 series from Palmer Station we show that elastic uplift alone cannot reproduce the cGPS
92 observations. A viscoelastic model is then used to predict uplift based on a range of Earth
93 models, and results are compared with the Palmer record to obtain the range of best fitting
94 models. Finally, the Earth model is further refined using six shorter cGPS time series from
95 the NAP (see Table 1).
96
97 2. Data
4
98 2.1. GPS
99 Fig. 1 shows the locations of available cGPS sites in the NAP. Of these, we used the
100 seven sites closest to the region of ice-mass change (see Table 1). Palmer is a long term
101 station with an excess of 15 years of data, and the remaining six sites were installed in 2009-
102 2010 as part of the LARISSA project (LARsen Ice Shelf System, Antarctica)
103 (http://www.hamilton.edu/expeditions/larissa). We did not use the record from O’Higgins (a
104 compilation of three records from two adjacent stations, OHIG, OHI2, OHI3; labelled OHI2
105 on Fig. 1) as a constraint as it lies far from the region of largest mass loss and as such may be
106 affected by potential lateral heterogeneity in Earth structure. Spring Point (Bevis et al., 2009)
107 (SPPT on Fig. 1) was also excluded due to the lack of data at this site; however we compare
108 our results with both of these records in the supplementary material.
109 The cGPS data from 1998 through to the end of 2012 were processed using a Precise
110 Point Positioning strategy (Zumberge et al., 1997) within GIPSY-OASIS v6.1.2.
111 Homogeneously reprocessed (as of 2012) satellite clocks and fiducial-free orbits were fixed
112 to values provided by the Jet Propulsion Laboratory. The receiver clocks, tropospheric zenith
113 wet delay, tropospheric gradients and station coordinates were estimated in standard ways
114 (e.g. Thomas et al., 2011). For the troposphere, we adopted the Vienna Mapping Function v1
115 (Boehm et al., 2006) and we assumed hydrostatic zenith delays based on the European Centre
116 for Medium-Range Weather Forecasts. Higher order ionospheric effects (Petrie et al., 2011)
117 were not corrected. Solid Earth tides were corrected according to the IERS 2010 conventions
118 (Petit and Luzum 2010) and ocean tide loading displacements were corrected based on the
119 TPXO7.2 ocean tide model (Egbert et al., 2009), which has been shown to perform very well
120 in this region (King et al., 2011), using the SPOTL software (Agnew 1996; Agnew 1997) in a
121 centre of mass of the whole Earth system (CM) reference frame (Fu et al., 2012). We fixed
122 carrier phase ambiguities to integers where possible (Bertiger et al., 2010). Observations were
5
123 weighted according to their elevation-dependent scatter from a preliminary, but otherwise
124 identical, solution.
125 Fiducial-free daily site coordinates were transformed into the ITRF2008 (Altamimi et al.,
126 2011) using a 6-parameter transformation and then corrected for changes in atmospheric
127 pressure loading using global 2.5 × 2.5 degree grids of loading, in a centre of figure of the
128 Earth (CF) reference frame, derived from the National Center for Environmental Protection
129 (NCEP) reanalysis surface pressure dataset (van Dam 2010). The correction was applied by
130 removing a daily average displacement with respect to a mean reference value. Large outliers
131 from the DUPT time series were manually identified and removed, and then a median filter
132 was applied to all time series. We only consider the height time series in this paper.
133 Velocities and realistic uncertainties were estimated using the CATS software (Williams
134 2008), along with annual and semi-annual harmonics. cGPS time series contain time-
135 correlated noise which inflates the true velocity uncertainties relative to the formal errors
136 obtained from a conventional linear regression. We consider a, now common, white noise
137 plus flicker noise model using the CATS software from which we determine velocity
138 uncertainties. We scale these to 2-sigma for subsequent use. Velocities and 2-sigma
139 uncertainties for each cGPS site are given in Table 1. Below we compare model output both
140 to the height time series and to vertical velocities derived from the time series. For
141 consistency, all model-predicted uplift rates were estimated over the same time period as the
142 cGPS observed uplift rate.
143 2.2. Ice-Mass Loss
144 The input ice load model is based on a dataset of elevation change derived from Digital
145 Elevation Model (DEM) differencing and ICESat data covering the NAP region north of
146 66°S. The time span of the data varies for different sub-regions. For the Larsen B tributary
147 glaciers data are available for two time periods, 2001-2006 (Shuman et al., 2011) and 2006-
6
148 2011 (Berthier et al., 2012). Comparing the two time-periods reveals differences in spatial
149 patterns of elevation change (Figs. 1b,c) but the overall estimated mass loss during these two
150 periods differs by less than 10% (Berthier et al., 2012). For the areas north and west of Larsen
151 B, the data span the period 2003-2009 (Scambos et al., 2014, in review). In all cases we take
152 the rate of ice-mass change as being constant throughout the respective data periods; we
153 discuss extrapolations to other time periods later.
154 The data were converted to a set of 17846 loading discs with areas between 0.9 and
155 1.1 km2 for input to the model, where the height of each disc represents a mass loss or gain,
156 using an ice density of 900 kg/m3 to convert to equivalent water height following Berthier et
157 al. (2012). Data gaps over large glaciers were infilled using an inverse distance weighting
158 algorithm (inpaint_nans within Matlab). Discs with very small mass change in the range
159 ±0.5 mweq/yr have a negligible effect on deformation at sites tens to hundreds of km distance
160 from the source of loading and were discounted from the ice load model to speed
161 computation time. This was tested using the best fitting Earth model and resulted in no more
162 than ±0.2 mm/yr differences in uplift rates at the cGPS sites. The resulting ice-mass change
163 model is shown in Fig. 1a with the two periods of mass change for Larsen B glaciers, 2001-
164 2006 and 2006-2011, shown separately in Figs. 1b and 1c, respectively. The uncertainty on
165 the elevation change dataset is ±1 m/yr (2-sigma) (Scambos et al., 2014, in review), and this
166 error bound was used to create upper and lower limits on our input ice load model.
167 The pattern of mass loss for glaciers feeding the former Prince Gustav and Larsen A ice
168 shelves prior to 2001 is not known. However, there is evidence that these glaciers reached
169 their current velocities within a few years of the breakup in 1995 (Rott et al., 2008), and this
170 velocity has been maintained 15 years after ice shelf collapse (Rott et al., 2011). Observations
171 of the glaciers feeding the more southern former Wordie Ice Shelf (Wendt et al., 2010),
172 which disintegrated in a series of events between 1966 and 1989, also suggest that high rates
7
173 of mass loss are sustained over decades. We therefore assume that the observed mass changes
174 for these northerly regions are representative of ice-mass loss from 1995 to the present-day.
175 We do not model any ice history before 1995, but instead take account of any ongoing
176 deformation related to ice-mass changes before this time by estimating a linear background
177 rate from the Palmer cGPS observations (see Section 3.1). In detail, we assumed that mass
178 loss in a region began at the half year mark after the collapse of the corresponding ice shelf
179 (i.e. 1995.5 for Prince Gustav and Larsen A glaciers, and 2002.5 for Larsen B glaciers), and
180 continued at the same rate to present-day (2013.0). For the Larsen B glaciers this is clearly
181 justified, as Scambos et al. (2004) show glacier acceleration and thinning commenced a few
182 months after ice shelf collapse. We assumed that the Larsen B tributary glaciers were not
183 losing significant mass before 2002.5 and set these discs to zero change between 1995.5 and
184 2002.5 accordingly. Any elevation changes that occurred away from former ice shelf regions
185 were assumed to be part of a multi-decadal trend and associated mass changes were applied
186 for the full modelling period. These were generally small and have little effect on our
187 modelling. Although widespread glacier retreat is seen on the western Peninsula (Cook et al.,
188 2005; Pritchard and Vaughan 2007), thinning appears to be generally limited to a small
189 section at the front of the glaciers and, importantly for this study, the pattern is changing
190 relatively slowly with time (Kunz et al., 2012). Because the Larsen A and Prince Gustav
191 glaciers are distant from our cGPS sites (150-300 km from Palmer), and the uplift signals due
192 to mass changes in these areas and on the western Peninsula are linear, errors in the above
193 mentioned assumptions have only a small effect on the conclusions drawn from our
194 modelling based on the non-linearity in the Palmer record.
195
196 3. Modelling
197 3.1. Elastic Modelling
8
198 The elastic uplift was computed with the elastic component of the software VE-HresV2
199 output (Visco-Elastic High Resolution technique for Earth deformations) (Barletta et al.,
200 2006) (Barletta et al., manuscript in preparation), which is based on a compressible,
201 spherically symmetric, self-gravitating Earth. Green’s functions were spatially convolved
202 with the ice loading discs according to the methods presented in Barletta et al. (2006). Load
203 Love numbers, based on the PREM Earth structure (Dziewonski and Anderson 1981), were
204 computed in the centre of mass reference frame up to a maximum spherical harmonic degree
205 of 3700 using VE-CL0V3RS v1.4 (Visco-Elastic Compressible LOVe numbER Solver)
206 (Barletta et al., in prep.) and the degree-1 Love number was computed as described by Spada
207 et al. (2011). By using the assumption that the elastic Love numbers become asymptotic after
208 the maximum degree, the software implementing the High Resolution technique allows us to
209 capture the loading concentrated on glaciers a few km wide (Barletta et al., 2006). In this
210 way, the resolution is limited only by the resolution of the input loading discs.
211 A time series of modelled elastic uplift was computed at the location of Palmer and
212 compared with the cGPS observations (Fig. 2). As the cGPS observations are recorded
213 relative to an arbitrary reference height and the model output is relative to zero uplift at the
214 start of the modelled time period, the cGPS observations have been offset to correct for this
215 based on their pre-2002 mean. To account for the effects of centennial- or millennial-scale
216 glacial isostatic adjustment (GIA) in the cGPS record we also estimated a ‘background’
217 vertical rate by subtracting the modelled elastic uplift rate from the cGPS uplift rate over the
218 linear part of the Palmer record (1998-2002). This gives the uplift rate due to any ice-mass
219 changes prior to the start of our ice loading model, assuming an elastic-only response to post-
220 1995 events. This rate was then included in our model-predicted time series so that model
221 output could be directly compared with cGPS observations.
222 3.2. Viscoelastic Modelling
9
223 The viscous uplift of the Earth in response to the ice-mass loss was computed using the
224 compressible viscous component of the software VE-HresV2 output, which uses VE-
225 CL0V3RS v1.4 to compute the elementary viscoelastic time-dependent Green’s functions
226 (convolved with Heaviside function) up to degree 1195, and assumes that at higher degrees
227 they do not change with time so the combined Green's function is negligible. This was
228 verified when choosing the maximum degree so that the results do not suffer from effects of
229 truncation and, as for the elastic modelling, we were able to capture the response from
230 glaciers a few km wide. We limit our study to a Maxwell rheological model. It is worth
231 noting that models with alternative and more complex rheologies may also sufficiently
232 explain the observations, however at present the dataset is too sparse to resolve or require
233 them; we return to this point in the discussion.
234 We adopt a four-layer viscosity structure consisting of an elastic lithosphere, and a
235 viscoelastic upper mantle, transition zone and lower mantle, as shown in Table 2. The density
236 structure of the model consists of 31 finer layers with densities from the PREM Earth
237 structure (Dziewonski and Anderson 1981). We define a simple four-layer viscosity model as
238 the limited data do not allow a more complex model to be resolved. This is discussed further
239 in Section 5.
240 We searched for the range of plausible best-fit Earth models by varying the lithospheric
241 thickness between 20 km and 160 km, and the upper mantle viscosity between 1 × 1017 and
242 1 × 1020 Pa s. Given that Simms et al. (2012) suggest a value of 1-2 × 1018 Pa s for the South
243 Shetland Islands, which lie closer to the active subduction zone than our study region, and
244 typical values of mantle viscosity proposed for Patagonia, Iceland, or Alaska are in the range
245 1 – 10 × 1018 Pa s (Auriac et al., 2013; Lange et al., 2014; Sato et al., 2011), mantle
246 viscosities below 1 × 1017 Pa s are not thought to be physically realistic for this region of the
247 Earth. All other parameters remained fixed. Below the upper mantle layer is a transition zone
10
248 between 400 and 670 km depth with a fixed viscosity of 4 × 1020 Pa s, as suggested by Sato et
249 al. (2011) in their study of the Earth’s response to ice-mass change in Alaska; and below this,
250 a lower mantle with a fixed viscosity of 1 × 1022 Pa s. Sensitivity to different mantle layer
251 thicknesses and a more complex Earth structure will be discussed later in Section 5.
252 3.3. cGPS Constraints
253 The uplift time series output from the viscous model were added to the modelled elastic
254 uplift and the background rate, which was recalculated as described in Section 3.1, this time
255 by subtracting the modelled viscoelastic uplift rate from the cGPS uplift rate between 1998
256 and 2002. The resulting uplift time series for each Earth model in the parameter space was
257 then compared, first of all, with the Palmer cGPS observations only. In order to determine the
258 range of Earth models consistent with our data, the RMS misfit between the modelled uplift
259 and the cGPS uplift was calculated and is shown in Fig. 3a.
260 In an attempt to place further constraints on the range of well-fitting Earth models, we
261 repeated the viscoelastic modelling to calculate uplift at the six LARISSA cGPS locations
262 (Fig. 1) for the full range of Earth models. By assuming that any lateral changes in Earth
263 structure are minimal over the distance spanned by the cGPS stations (a maximum of
264 300 km), all sites can be used as constraints on a 1-D Earth model. The RMS misfit was
265 computed again by comparing the model-predicted uplift (viscoelastic + background) with
266 the cGPS observed uplift at all seven stations. When computing the modelled time series at
267 the LARISSA stations, which were not occupied prior to the Larsen B break-up, we assumed
268 that the background rate previously calculated for Palmer was representative of the whole
269 region. That is, we assumed a spatially constant background rate across all seven cGPS sites;
270 this is supported by the closeness of fit of the initial Palmer-constrained model to most of the
271 LARISSA sites (residual uplift rates in Table 3). Our assumption implies that the sites would
272 have been uplifting at lower rates prior to 2002 and the time series would be non-linear,
11
273 similar to that observed at Palmer. The implications of assuming a spatially-constant
274 background rate are discussed later in Section 5.1. At present, we do not attempt to include
275 geologic constraints on the background uplift rate, such as from marine limits and deglacial
276 chronologies, as most sites (but not all) lack evidence suitable for long-term estimates of
277 glacial isostatic adjustment.
278
279 4. Results
280 4.1. Elastic Modelling
281 The Palmer cGPS record displays significant non-linearity after 2002; however, the
282 results of the elastic modelling show that even within the uncertainty bounds of the ice-mass
283 change data (±1 m/yr), these changes in rate cannot be explained by elastic uplift only. In
284 fact, more than five times the amount of observed mass loss (i.e. five times the mass loss
285 shown in Fig. 1, applied to each disc) would be required to reproduce the magnitude of the
286 observed uplift (modelled uplift shown by the green line in Fig. 2). This is not plausible and
287 so we reject the possibility of missing ice unloading in our model, as the missing mass would
288 not only need to be large, or be very close to Palmer, but also sustained from 2002 to present.
289 Such a large signal would require a major ice shelf collapse or substantial glacier mass-loss
290 adjacent to Palmer and neither scenario exists. Consequently, we conclude that less than half
291 of the rapid increase in uplift at Palmer can be accounted for by elastic rebound, and examine
292 if additional viscous uplift may help explain the remaining cGPS uplift signal.
293 4.2. Viscoelastic Modelling Constrained by PALM
294 The RMS misfit between the modelled uplift and the Palmer cGPS uplift is shown in Fig.
295 3a. The best fitting Earth models, lying within the 95% confidence limit of observational
296 residuals, have a lithospheric thickness in the range 20-160 km and an upper mantle viscosity
297 in the range 1 × 1017 - 2 × 1018 Pa s. There is some trade-off between the two parameters,
12
298 with thicker lithosphere models accompanying a lower viscosity mantle and vice versa. The
299 Earth model with the lowest RMS misfit (4.67 mm) has values of 130 km and 7 × 1017 Pa s.
300 Computing the RMS again with a shortened time series ending in 2011 to coincide with the
301 ice-mass change data, results in a best fitting model with a lithospheric thickness of 20 km.
302 There is a possible offset in the Palmer time series during 1999 and only using data after this
303 time (and recomputing the background rate appropriately) results in a best fitting model with
304 a lithospheric thickness of 30 km. This highlights that the lithospheric thickness is poorly
305 constrained within our model, although the upper mantle viscosity is robustly found to be less
306 than 2 × 1018 Pa s in all cases.
307 For the Earth model with lowest RMS misfit to the Palmer time series, we compared the
308 model-predicted velocities at all cGPS sites with observed velocities (Table 3). The model
309 over-predicts uplift at CAPF by 2.8 mm/yr (compared with a 2-sigma uncertainty of
310 2.9 mm/yr) and under-predicts uplift at DUPT by 2.4 mm/yr, which is the only significant
311 residual, but the misfit here is only ~23% of the modelled uplift. The model performs well at
312 the other four LARISSA sites with misfits in uplift rate <2 mm/yr and within the 2-sigma
313 observational error.
314 4.3. Viscoelastic Modelling Constrained with all cGPS Records
315 Constraining the Earth model using uplift data from only one cGPS location results in an
316 upper mantle viscosity that is relatively well constrained, but with a broad range of
317 acceptable values of lithospheric thickness. Fig. 3b shows the RMS misfit between modelled
318 uplift and the cGPS observed uplift for all sites. When using all the cGPS data to constrain
319 the Earth models, the range of lithospheric thickness for the best fitting models narrows to
320 100–140 km and the acceptable range of upper mantle viscosity narrows to 6 × 1017 – 2 ×
321 1018 Pa s, as indicated by the 95% confidence limit. The Earth model with the lowest RMS
322 misfit (4.38 mm) has values of 120 km and 1 × 1018 Pa s.
13
323 The model-predicted time series for the best fitting Earth models in Figs. 3a and 3b are
324 plotted against the cGPS time series in Fig. 4. For comparison, predicted time series using the
325 “VM2” Earth model, the viscosity structure which accompanies the global ICE-5G GIA
326 model (Peltier 2004), are also plotted, along with time series calculated using an Earth model
327 within the ranges suggested by Ivins et al. (2011) (an incompressible model as used in (Ivins
328 et al., 2011) with 40 km lithosphere and 3 × 1019 Pa s upper mantle viscosity). There is little
329 difference between our two best fit models, whereas both VM2 and the Ivins et al. (2011)
330 models under-predict uplift at all cGPS locations. The uplift predicted by the VM2 and Ivins
331 models is dominated by the elastic part of the signal, and the viscous contribution is small.
332 For example, at FONP the viscous part of the total uplift at 2013.0 is 22 mm for the Ivins et
333 al. (2011) model, and only 1 mm for VM2, compared with 123-130 mm for our best fitting
334 models. In the supplementary material we compare the model-predicted uplift with GPS
335 records at two further locations: OHI2 and SPPT (see Fig. 1 for locations), and this is
336 discussed in Section 5.
337 The spatial distribution of model-predicted uplift rates (estimated over the same time
338 period as the cGPS observed uplift rate, i.e. 2009.0 – 2013.0) for the elastic and viscous
339 components are shown in Figs. 5a and 5b, respectively, the latter based on the best-fitting
340 Earth model from Fig. 3b, as constrained by all seven cGPS sites. Fig. 5c shows the sum of
341 panels a and b and represents the viscoelastic uplift rates including the uniform background
342 rate, with cGPS uplift rates over-plotted (as per Table 3). The observed cGPS uplift rates are
343 well reproduced by the model.
344
345 5. Discussion
346 5.1. Earth Model
14
347 Using the ice-mass change dataset and observations from seven cGPS stations we have
348 been able to constrain a range of Earth models for the NAP. We first used Palmer station only
349 to constrain the Earth model, as the background uplift rate due to long-term glacial isostatic
350 adjustment is well constrained by the pre-2002 data, available only at this site. The addition
351 of the six LARISSA cGPS sites narrows the overall range of best fitting Earth models to a
352 lithospheric thickness between 100 km and 140 km and upper mantle viscosity in the range
353 6 × 1017 – 2 × 1018 Pa s. Using a uniform background rate for the whole region may introduce
354 some error in these results if the signal is in fact spatially variable, as suggested by Nield et
355 al. (2012). Nonetheless, using the LARISSA cGPS data provides some verification for the
356 inferences from the Palmer dataset. To test the sensitivity to a spatially constant background
357 rate, we computed a new background rate based on that estimated from Palmer, but scaled at
358 the other cGPS locations according to the spatial pattern of the W12a Antarctic GIA model
359 (Whitehouse et al., 2012). Computing the RMS again for all cGPS sites does not change the
360 best fitting model and reduces the minimum RMS misfit by only 0.01 mm, giving further
361 confidence in our results. Furthermore, comparing the best fitting model-predicted uplift with
362 campaign GPS observations between 1997 and 2013 at the location of Spring Point, which
363 were not included as constraints on the model, shows a qualitatively good fit and strengthens
364 our conclusions (Fig. S3 in the supplementary material).
365 The Earth model with minimum RMS misfit in both cases (Figs. 3a and 3b) has a thick
366 lithosphere (120-130 km) and a low upper mantle viscosity (7 × 1017 – 1 × 1018 Pa s).
367 However, it is important to note that the solution is non-unique and within the 95%
368 confidence limit the RMS misfit varies by less than 1 mm, so any model within this limit can
369 provide a reasonable fit to the data. The combination of thick lithosphere and low upper
370 mantle viscosity is somewhat unexpected, as low viscosity regions are commonly
371 accompanied by a thinner lithosphere (e.g. Auriac et al., 2013; Lange et al., 2014; Simms et
15
372 al., 2012). However, as described in Section 4.2, computing the RMS misfit of Palmer using
373 only pre-2011 data gives a best fitting lithospheric thickness of 20 km, which highlights our
374 poor sensitivity to lithospheric thickness. Similarly, when discounting data before 1999.5
375 which may be affected by a possible offset in the Palmer time series, the best fitting
376 lithospheric thickness is reduced to 30 km. In contrast, we robustly determine an upper
377 mantle viscosity of less than 2 × 1018 Pa s (the upper limit of the 95% confidence interval) is
378 required to fit the available data. A low viscosity upper mantle is consistent with the back-arc
379 setting and evidence of recent volcanism in the region.
380 Our range of Earth models is different to those determined by Ivins et al. (2011) for a
381 larger region encompassing ours. Fig. 4 reveals that the Ivins et al. (2011) Earth model, when
382 combined with post-1995 ice unloading, cannot explain the rapid uplift at Palmer since 2002.
383 There are a number of possible reasons for this. First, Ivins et al. (2011) considered a single
384 Earth model for a region approximately three times larger than ours, and hence their model is
385 an average for this wider region. Second, the ice unloading scenarios considered by Ivins et
386 al. (2011) are based on relatively few observations and their Earth model may be
387 compensating for ice load errors in poorly constrained regions. Third, Ivins et al. (2011) were
388 limited in their ability to consider the non-linearity in the Palmer record, as their analysis
389 required them to combine it with the GRACE time series which started after 2002, and
390 therefore they treated it as a single linear rate over the post-2002 data period. Finally, it needs
391 to be verified if our Earth model could satisfactorily fit the observations of the kind used by
392 Ivins et al. (2011); if it cannot, then this may be an indication that use of higher-order
393 constitutive theories that exhibit non-linear creep response functions (see Ivins and Sammis
394 (1996), Figure 7 therein), and whose material parameters may be independently tested by
395 both laboratory and geophysical observation, must be considered.
16
396 The peak uplift predicted by our best fit Earth model is 47 mm/yr located in the
397 Hektoria/Green glacier basin (Fig. 5c), corresponding to the geographical location of the
398 largest mass loss (Berthier et al., 2012). The peak uplift is dominated by the elastic signal and
399 has a small spatial extent, diminishing to 30 mm/yr or less within ~30 km. Our nearest cGPS
400 site is located at Foyn Point (FONP), ~40 km away, where the observed uplift rate of 14.9 ±
401 2.7 mm/yr agrees well with the 16.4 mm/yr predicted by the model. Our rates may differ
402 from the true uplift for parts of the model domain if the long-term background uplift rate is
403 substantially different to the spatially constant term we have adopted; however, the closeness
404 of the fit between the LARISSA cGPS data and our model predictions suggests our first
405 approximation is reasonable.
406 5.2. Lateral Variations in Earth Structure
407 In using a 1-D symmetric Earth model we do not consider the effects of lateral
408 heterogeneity in Earth structure. As our study region is small, there are unlikely to be large
409 variations within the area covered by the cGPS stations. However, the long-term tectonic
410 history of the region suggests that there may be a gradient in Earth structure along the length
411 of the Peninsula (Barker 2001; Larter et al., 1997). This is supported by the recent study of
412 Simms et al. (2012) who predict a thinner lithosphere (15km) for the South Shetland Islands,
413 which lie 100 km off the northern tip of the AP. Due to the likely lateral variations in Earth
414 structure, we did not include any cGPS data far from the site of largest ice loss as constraints
415 (e.g. O’Higgins which lies 300 km to the north, OHI2 in Fig. 1), although we compare the
416 model-predicted uplift to these cGPS observations in Fig. S2 of the supplementary material.
417 Fig. S2 shows that the linear uplift recorded at O’Higgins cannot be explained by our model,
418 both in terms of the magnitude of uplift and linearity of the time series. This is likely due to a
419 combination of increased uncertainty in ice unloading near to O’Higgins over 1995-2001, the
420 different Earth structure and our assumption of a spatially constant background rate.
17
421 The Earth models inferred here show that the NAP cannot successfully be modelled as
422 part of a continent-wide GIA model, as the Earth structure is too different from that
423 traditionally used for the rest of Antarctica (e.g., Whitehouse et al., 2012). Our work has
424 important implications for forthcoming GIA models which incorporate 3-D Earth structure,
425 and it identifies a location where upper Earth structure may be constrained by observations.
426 5.3. Sensitivity to a Complex Earth Structure
427 We found that the cGPS observations can be explained reasonably well by a simple four-
428 layer viscous model, in which only the lithospheric thickness and upper mantle viscosity
429 parameters were varied. The depth over which the load induces mantle flow was tested by
430 decreasing the depth of the modelled upper mantle-transition zone boundary to 350 km. The
431 RMS of the two best fit models increased by 6-11% suggesting that mantle flow occurs to at
432 least this depth. Increasing or decreasing the transition zone viscosity by an order of
433 magnitude made less than 1% difference to the RMS for each best fit model. Our results are,
434 therefore, not sensitive to changes in Earth model parameters below 400 km depth due to the
435 small spatial extent of the load and observations. In view of this we consider the implications
436 of an Earth model with a more complex structure in the top 400 km.
437 Several studies that have used a more complex Earth structure include a low viscosity
438 zone (LVZ) directly beneath the elastic lithosphere (e.g., Sato et al., 2011). We performed
439 some sensitivity tests to investigate whether such a model could provide a better fit to the
440 data. Two thicknesses of the LVZ were tested (100 km and 200 km), along with several
441 different ratios of LVZ viscosity to upper mantle viscosity (1:5, 1:10, 1:20) (six experiments
442 in total). The results showed that whilst the single best fitting Earth model changed for each
443 experiment, the overall range within the 95% confidence limit remained broadly the same.
444 Furthermore, the minimum RMS misfit did not improve by more than 1%, demonstrating that
445 a significantly better fit to the data could not be achieved with a more complex Earth model.
18
446 A more spatially extensive cGPS network might in the future enable a more complex
447 Earth structure and lateral variations to be resolved and this network expansion is currently
448 underway as an extension of the LARISSA project, with a permanent site now installed at
449 Spring Point.
450 5.4. Sensitivity to Ice Model Uncertainties
451 As described in Section 2, we modelled ice-mass change over a longer time period than is
452 covered by the elevation change data by linearly extrapolating a constant rate of ice loss
453 backwards and forwards in time from a few months after ice shelf break up to the present
454 day, with no ramp up of mass change included. Studies have suggested that glaciers in the
455 NAP that have accelerated following an ice shelf collapse remain at elevated speeds for
456 decades. Rott et al. (2008) showed that Drygalski glacier, feeding the former Larsen A Ice
457 Shelf, did not accelerate between 1999 and 2007, and Rott et al. (2011) state that the
458 increased velocity of the Larsen A and Prince Gustav glaciers has so far been maintained 15
459 years after ice shelf collapse. The uncertainties in our ice model therefore relate to how
460 quickly Larsen B glaciers accelerated to reach the 2002-2006 rates (Fig. 1b), and the
461 acceleration history of Larsen A and Prince Gustav glaciers between 1995 and 1999.
462 To investigate this we simulated the acceleration of the glaciers in our ice loading model
463 by linearly increasing the rate of mass loss from 0 mweq/yr at the time of ice shelf collapse, to
464 full rates (as shown in Fig. 1) one year later for Larsen B and Larsen A/Prince Gustav
465 glaciers separately. For Larsen B glaciers this ramp up scenario of ice-mass loss improved the
466 RMS misfit by less than 5%, and similarly for Larsen A and Prince Gustav glaciers,
467 confirming that the effect of errors in our ice loading assumptions is small.
468 5.5. Elastic Effects of Surface Mass Balance Anomalies
469 Whilst the model output closely matches the cGPS time series overall, there are localised
470 misfits. This is likely due to local time variable mass changes which are not included in our
19
471 ice loading model. We investigated the possibility that these fluctuations are caused by an
472 elastic response to variations in surface mass balance (SMB) over shorter periods of time than
473 the DEMs allow us to resolve. SMB is dominated by iceberg calving, some melt runoff, and
474 accumulation.
475 Using the RACMO2.1/ANT27 dataset of SMB up to 2011.0 (Lenaerts et al., 2012), we
476 removed the long term trend to obtain anomalies to the mean at each grid point, and
477 converted them to a set of loading discs. The elastic response to the SMB anomalies was
478 calculated at Palmer, and superimposed onto the time series for the best fit viscoelastic model
479 from Fig. 3a. We perform this calculation with some caution due to the low resolution of the
480 SMB model (27km) compared with the small valley glaciers that dominate much of this
481 region (Trusel et al., 2013). Nevertheless, Fig. 6 shows that the additional elastic response
482 improves the fit between the modelled and observed time series and explains most of the
483 short-term variations, which likely reflect seasonal signals and multi-year perturbations in
484 SMB. The RMS misfit, calculated over the shorter time period of the SMB model, reduces
485 marginally from 4.74 mm to 4.56 mm. It is not known how the effect of SMB anomalies
486 could improve the fit at the other cGPS sites as the RACMO2.1/ANT27 model output is
487 presently only available up until the end of 2010, providing minimal overlap with the
488 LARISSA time series. A viscous response to SMB load changes is feasible but was not
489 considered, as due to the fluctuating nature of the SMB loads it is likely to be small.
490
491 6. Conclusions
492 Non-linear cGPS observed uplift from the NAP cannot be explained by the elastic
493 response of the Earth to ice-mass loss events relating to Larsen A, Prince Gustav, and
494 Larsen B ice shelf break-up.
20
495 A linear Maxwell viscoelastic model can produce a good fit to the Palmer cGPS
496 record, which constrains the upper mantle viscosity to less than 2 × 1018 Pa s, but the
497 lithospheric thickness remains poorly constrained.
498 Shorter time series from the six cGPS stations of the LARISSA network verify this
499 result, finding a best fitting Earth model with an upper mantle viscosity of 6 × 1017 –
500 2 × 1018 Pa s and narrowing the lithospheric thickness to 100–140 km, although the
501 analysis is limited by the assumption of a spatially uniform background rate.
502 A more complex Earth structure, in terms of vertical stratification, could explain the
503 observed data equally well, but additional cGPS stations are required to resolve this
504 structure further.
505 Reconciliation of present-day rates of bedrock uplift with average rates over longer
506 timescales may require rheological models that exhibit a non-linear response.
507 In regions of low upper mantle viscosity and on-going ice-mass change, cGPS data
508 cannot be correctly interpreted without considering the viscoelastic response to
509 present-day ice-mass change.
510
511 Acknowledgements: G.A.N. is supported by a NERC PhD studentship, M.A.K. is a recipient
512 of an Australian Research Council Future Fellowship (project number FT110100207), and
513 P.L.W. is a recipient of a NERC Independent Research Fellowship. VE-CL0V3RS was
514 developed by V.R.B and A.B in a self-funded project. Installation of the LARISSA cGPS
515 network was supported by NSF grant OPP-ANT-0732467 to EWD while data acquisition and
516 station vitality are supported by UNAVCO. Support of field logistics for station installation
517 was provided by the crew and staff aboard the USAP vessels L.M. Gould and N.B. Palmer;
518 we thank them and LARISSA colleagues for invaluable assistance. E.B. acknowledges
519 support from the French Space Agency (CNES) through the TOSCA and ISIS programs.
21
520 SPOT5 DEM were provided by the SPIRIT project (Korona et al., 2009) funded by the
521 French Space Agency (CNES). We acknowledge Christopher Shuman of the University of
522 Maryland, Baltimore County and Terry Haran of NSIDC for their contributions to the
523 elevation change data set. We also thank Michael Bevis for helpful discussions on the Palmer
524 time series, and Michiel van den Broeke and Jan Lenaerts for providing SMB output from
525 RACMO2.1/ANT27. Figures have been generated using the GMT software (Wessel and
526 Smith 1998). Erik Ivins and an anonymous reviewer are thanked for their comments that
527 helped clarify and improve the manuscript.
528
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699
700
29
701 Figures
702
703 Fig. 1. Observed ice-mass change rate given in metres water equivalent per year. a) The full
704 study area with cGPS locations shown as pink circles and former ice shelf locations as dashed
705 black lines (Prince Gustav (PG), Larsen A (LA) and Larsen B (LB)). Values in the Larsen B
706 area (see Fig. 1b) represent the mean rate of change for the period 2001-2006, values
707 elsewhere represent the mean rate of change for the period 2003-2009. Inset shows location
708 of the study area. b) Ice-mass change for Larsen B only using 2001-2006 data. c) Ice-mass
709 change for Larsen B only using 2006-2011 data. H-G is the Hektoria-Green drainage basin.
710
30
711 Fig. 2. Palmer cGPS observations (grey dots) compared with uplift time series predicted by
712 the elastic model (red line). Predicted elastic uplift time series for upper and lower bounds on
713 ice-mass loss is shown by the orange dashed lines; and predicted uplift time series assuming
714 5 times the observed ice-mass loss is shown by the green line with squares.
715
716
31
717 Fig. 3. RMS misfit between modelled viscoelastic uplift time series and cGPS observed time
718 series for a) Palmer only, and b) Palmer and all stations of the LARISSA network. The 95%
719 confidence limit is plotted as a solid black line, and the best fit Earth model in each case is
720 plotted as a red star.
721
722
32
723 Fig. 4. cGPS observations (grey dots) and model-predicted uplift time series at each cGPS
724 location for: the best fitting viscoelastic Earth model in Fig. 3a (red line), the best fitting
725 viscoelastic Earth model in Fig. 3b (blue squares), the Ivins et al. (2011) viscoelastic Earth
726 model (orange line), and the VM2 viscoelastic Earth model (green dashed line). Map shows
727 cGPS locations.
728
33
729 Fig. 5. Uplift rates at 2011 for the best fitting viscoelastic Earth model in Fig. 3b; (a) elastic
730 only, (b) viscous only, and (c) combined viscoelastic and background rate. Post-2009 cGPS
731 uplift rates are plotted as circles using the same colour scale.
732
733 Fig. 6. Palmer cGPS observations (grey dots) and model-predicted uplift time series for the
734 best fitting Earth model in Fig. 3a (red line), and the best fitting Earth model with the
735 addition of the elastic effects of SMB anomalies (pale blue line).
736
34
737 Tables
738
739 Table 1: Location of cGPS stations, observing period, and observed uplift velocities.
Site Latitude (°) Longitude (°) Observing Period cGPS Observed Uplift (mm/yr) Palmer -64.78 -64.05 1998.5 – 2013.0 6.6 ± 2.1 (PALM) (2009.0‒2013.0 only) Cape Framnes -66.01 -60.56 2010.1 – 2013.0 (CAPF) 4.5 ± 2.9 Duthier’s -64.81 -62.82 2009.3 – 2013.0 Point (DUPT) 12.8 ± 2.1 Foyn Point -65.25 -61.65 2010.1 – 2013.0 (FONP) 14.9 ± 2.7 Hugo Island -64.96 -65.67 2009.3 – 2013.0 (HUGO) 1.7 ± 3.3 Robertson -65.25 -59.44 2010.1 – 2013.0 Island (ROBI) 7.8 ± 2.9 Vernadsky -65.25 -64.25 2010.1 – 2013.0 (VNAD) 5.8 ± 2.4 740
741 Table 2: Earth model parameters, with those that have been varied underlined.
Depth to base (km) Viscosity (Pa s)
Lithosphere 20 – 160 km 1 x 1051
Upper Mantle 400 1 x 1017 – 1 x 1020
Transition Zone 670 4 x 1020
Lower Mantle - 1 x 1022 742
743
35
744 Table 3: cGPS observed uplift velocities with 2-sigma error; model-predicted uplift
745 velocities for the elastic only model and the best fitting viscoelastic model from Fig. 3a. Both
746 model-predicted uplift velocities include the estimated background rate. Last column shows
747 the residual between observed and modelled viscoelastic uplift.
Residual (cGPS cGPS Observed Uplift Elastic Modelled Viscoelastic Modelled Site minus viscoelastic (mm/yr) Uplift (mm/yr) Uplift (mm/yr) model) (mm/yr) 6.6 ± 2.1 PALM 1.5 7.9 -1.3 (2009.0‒2013.0 only) CAPF 4.5 ± 2.9 0.4 7.3 -2.8
DUPT 12.8 ± 2.1 1.7 10.4 2.4
FONP 14.9 ± 2.7 6.7 16.4 -1.5
HUGO 1.7 ± 3.3 -0.4 2.8 -1.1
ROBI 7.8 ± 2.9 1.0 9.8 -2.0
VNAD 5.8 ± 2.4 0.01 5.9 -0.1 748
749
750
36
751 Supplementary Material
752 Fig. S1. Bathymetry of the study region showing the location of the active subduction zone
753 (South Shetland Trench), the Bransfield Basin and the Passive Margin. cGPS locations are
754 shown in red. Bathymetry data is taken from Arndt et al. (2013).
755 Arndt, J.E., Schenke, H.W., Jakobsson, M., Nitsche, F.O., Buys, G., Goleby, B., Rebesco,
756 M., Bohoyo, F., Hong, J., Black, J., Greku, R., Udintsev, G., Barrios, F., Reynoso-Peralta,
757 W., Taisei, M., Wigley, R. 2013, The International Bathymetric Chart of the Southern Ocean
758 (IBCSO) Version 1.0—A new bathymetric compilation covering circum-Antarctic waters,
759 Geophysical Research Letters, 40(12), 3111-3117, doi: 10.1002/grl.50413.
760
37
761 Fig. S2. cGPS observations (dots) and model-predicted uplift time series at O’Higgins for the
762 best fitting viscoelastic Earth model in Fig. 3a (red line) and the best fitting viscoelastic Earth
763 model in Fig. 3b (blue squares). The model-predicted uplift includes the background rate
764 derived from Palmer. The O’Higgins cGPS time series is made up of OHIG (dark grey dots),
765 and its replacement antenna OHI2 (light grey dots). OHI3, from the adjacent station, is also
766 shown (offset) in the orange dots. Note that the O’Higgins time series was not used to
767 constrain the Earth model.
768
769
38
770 Fig. S3. Campaign GPS observations (grey dots) with error bars and model-predicted uplift
771 time series at Spring Point (SPPT) for the best fitting viscoelastic Earth model in Fig. 3a (red
772 line) and the best fitting viscoelastic Earth model in Fig. 3b (blue squares). The model-
773 predicted uplift includes the background rate derived from Palmer. Note that the Spring Point
774 time series was not used to constrain the Earth model.
775
39